Unconventional Spectral Gaps Induced by Charge Density Waves in the Weyl Semimetal (TaSe4)2I

Coupling Weyl quasiparticles and charge density waves (CDWs) can lead to fascinating band renormalization and many-body effects beyond band folding and Peierls gaps. For the quasi-one-dimensional chiral compound (TaSe4)2I with an incommensurate CDW transition at TC = 263 K, photoemission mappings thus far are intriguing due to suppressed emission near the Fermi level. Models for this unconventional behavior include axion insulator phases, correlation pseudogaps, polaron subbands, bipolaron bound states, etc. Our photoemission measurements show sharp quasiparticle bands crossing the Fermi level at T > TC, but for T < TC, these bands retain their dispersions with no Peierls or axion gaps at the Weyl points. Instead, occupied band edges recede from the Fermi level, opening a spectral gap. Our results confirm localization of quasiparticles (holes created by photoemission) is the key physics, which suppresses spectral weights over an energy window governed by incommensurate modulation and inherent phase defects of CDW.


(TaSe4)2I single crystals and cleavage
Figure S1a shows as-grown single crystals of (TaSe4)2I stored under inert gas in a glass container.The crystals, with a quasi-one-dimensional atomic structure, have needle-like shapes and tend to break along the (110) surfaces after cleavage.Figure S1b shows a sample after cleavage.The surface appears corrugated, which, however, does not affect ARPES band mapping along the Z chain direction.Each sample for ARPES measurements is attached to a copper plate using silver epoxy to ensure good thermal conductivity.

Sample characterization
The (TaSe4)2I material was characterized by x-ray diffraction and resistivity measurements.
As shown in Fig. S2a, CDW satellite peaks emerge as the sample temperature is lowered below TC.Plotted in Fig. S2b

Temperature-dependent ARPES intensity of band A in (TaSe4)2I
Figure S3 shows ARPES intensity of band A (Fig. 1) as a function of energy at various temperatures.The intensity for each temperature is normalized by its maximum within the selected energy range (-0.4 to 0.1 eV).The results show a rapid reduction beginning at about -0.38 eV, reaching 50% at around -0.28 eV for the entire temperature range.The intensity is extremely low at the Fermi level at E = 0.    the energy range of 0 to -1 eV and the momentum range of 0 to 0.5 Å -1 (this region is indicated in Fig. S6b-S9b).There are substantial variations over the imaged area for each polarization configuration.The fractional variation II 

Spatial mapping and polarization dependence of ARPES maps
(root mean square deviation from the mean normalized by the mean) is 14%, 10%, 14%, and 12% for the LV, LH, CR, and CL polarization configurations, respectively.It is interesting to note that the spatial features of the four images show some correlations but are not identical.A likely reason for the complexity is surface roughness (Fig. S1).Theoretically, ARPES intensities can depend strongly on the surface orientation relative to the electric field of the incident beam 1 .For a rough surface, the polarization dependence can become quite complex.Figures S6b-S9b
is the intensity of the satellite peak as a function of temperature.The results indicate a transition temperature of TC = 263 K.The sample resistivity measured along the chain direction as a function of temperature, shown in Fig. S2c, shows a subtle change in slope around TC. Upon taking the logarithmic derivative of the data, a sharp peak is seen at 263 K.These results confirm the transition temperature at TC = 263 K, in agreement with the accepted value in the literature.

Figure
Figure S2 Sample characterization.a Line cuts of temperature-dependent x-ray diffraction taken

Figure S3
Figure S3 Temperature dependence of ARPES intensity of band A. The blue and green dotted

Figure S4 a
Figure S4 a ARPES map taken at 105 K with 25-eV photons.b EDCs taken at kz = 0.25 Å -1 as a

Figure
FigureS5shows the experimental geometry for spatial mapping with four different

Figure
Figure S5 Polarization configuration for spatial mapping.a For linearly polarized light.b For Figs. S6-S9c-f.Evidently, the observed band dispersion relations are the same for the different

Figure
Figure S6 ARPES maps taken with linear vertically polarized light at 51 eV. a Spatial mapping

Figure
Figure S7 ARPES maps taken with linear horizontally polarized light.Same as Fig. S6 except

Figure
Figure S8 ARPES maps taken with right circularly polarized light.Same as Fig. S6 except for

Figure
Figure S9 ARPES maps taken with left circularly polarized light.Same as Fig. S6 except for